Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives

被引:33
作者
Abdeljawad, Thabet [1 ]
Agarwal, Ravi P. [2 ]
Alzabut, Jehad [1 ]
Jarad, Fahd [3 ]
Ozbekler, Abdullah [4 ]
机构
[1] Prince Sultan Univ, Dept Math & Gen Sci, Riyadh, Saudi Arabia
[2] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX USA
[3] Cankaya Univ, Dept Math, Ankara, Turkey
[4] Atilim Univ, Dept Math, Ankara, Turkey
关键词
Lyapunov inequality; Hartman inequality; Conformable derivative; Green's function; Boundary value problem; Mixed non-linearities;
D O I
10.1186/s13660-018-1731-x
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.
引用
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页数:17
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